Local versus long-distance Fission in Distributed Morphology

[GPMcG06]: the verbal agreement suffixes of Yucatec Maya come from one node, Agr3, which agrees with both the ergative subject and the nominative object and is realized by strict scansion of the Vocabulary (27) with local Fission — an item discharges its features from one of the node's two matrices and the residue stays available to the items below. The second- and third-person plural suffixes -éːʃ and -oʔob are unspecified for case, so their order is fixed by specificity, -éːʃ before -oʔob whatever the grammatical roles ((19)–(22)), and one scansion never inserts -oʔob twice ((23)–(24)); the object–subject template (18) gets both wrong. Long-distance Fission is rejected: the split of ergative person onto the auxiliary (Agr1, (43)) and number onto the verb runs across a word boundary, and first-person number is a person distinction ((42), on the feature-geometric treatment of first person).

Main definitions

• matrix, ergMatrix: an argument's matrix over Minimalist.FeatureVal — the person features of (26) from Person.toFeatures, number, and case.
• agr3, agr1, agr2: the Vocabularies (27), (43), (44).
• suffixes: Agr3's exponents for a subject and an object, by scansion.
• templateSuffixes: the rival template (18), one node per argument.

Main results

• suffixes_rows: every row of the pool is grammatical iff its suffixes are suffixes' output.
• template_predicts_starred, template_fails_grammatical: the template predicts the starred orders of (21) and (23) and fails (22) and (24).
• aux_prefix_rows: (43) and (44) recover the auxiliary suffix and the verbal prefix of every row.
• first_person_no_verbal_number: a first-person ergative argument takes no verbal number suffix ((3)–(4)), since its number is not [+Pl].

Implementation notes

Agr3's list (27) needs the nominative first-person plural to carry [+PSE] and the singular not to, the reverse of the assignment (42) gives the ergative auxiliary; the paper does not reconcile the two, so matrix follows (27) for nominative first person and (42) otherwise. The elsewhere -Ø is inserted but not counted among a row's overt suffixes.

References

• H. Harley and E. Ritter, Person and number in pronouns

Features and matrices (§3–4)

def GonzalezPootMcGinnis2006.personFeatures (p : Person) : List Minimalist.FeatureVal

The person features of (26), [±PSE, ±Auth], as the substrate's [±participant, ±author] decomposition of a person.

Equations

• GonzalezPootMcGinnis2006.personFeatures p = match p.toFeatures with | some f => [Minimalist.FeatureVal.participant f.hasParticipant, Minimalist.FeatureVal.author f.hasAuthor] | none => []

def GonzalezPootMcGinnis2006.number (pl : Bool) : Minimalist.FeatureVal

Number as [±Pl]: plural or singular.

Equations

• GonzalezPootMcGinnis2006.number pl = Minimalist.FeatureVal.phi (Minimalist.PhiFeature.number (if pl = true then Number.plural else Number.singular))

def GonzalezPootMcGinnis2006.ergMatrix : Person → Bool → List Minimalist.FeatureVal

An ergative argument's matrix ((42)): first-person number is a person distinction — singular [+PSE, +Auth], plural [+Auth].

Equations

• GonzalezPootMcGinnis2006.ergMatrix Person.first false = [Minimalist.FeatureVal.participant true, Minimalist.FeatureVal.author true, Minimalist.FeatureVal.case Case.erg]
• GonzalezPootMcGinnis2006.ergMatrix Person.first true = [Minimalist.FeatureVal.author true, Minimalist.FeatureVal.case Case.erg]
• GonzalezPootMcGinnis2006.ergMatrix x✝¹ x✝ = GonzalezPootMcGinnis2006.personFeatures x✝¹ ++ [GonzalezPootMcGinnis2006.number x✝, Minimalist.FeatureVal.case Case.erg]

def GonzalezPootMcGinnis2006.matrix : Person → Bool → Case → List Minimalist.FeatureVal

An argument's matrix for Agr3: (42) for ergative arguments and for second and third person; for nominative first person the assignment (27) presupposes — -oʔon 1pl [+PSE, +Auth, NOM], -en 1sg [+Auth, NOM].

Equations

• GonzalezPootMcGinnis2006.matrix Person.first false Case.nom = [Minimalist.FeatureVal.author true, Minimalist.FeatureVal.case Case.nom]
• GonzalezPootMcGinnis2006.matrix Person.first true Case.nom = [Minimalist.FeatureVal.participant true, Minimalist.FeatureVal.author true, Minimalist.FeatureVal.case Case.nom]
• GonzalezPootMcGinnis2006.matrix x✝¹ x✝ Case.erg = GonzalezPootMcGinnis2006.ergMatrix x✝¹ x✝
• GonzalezPootMcGinnis2006.matrix x✝² x✝¹ x✝ = GonzalezPootMcGinnis2006.personFeatures x✝² ++ [GonzalezPootMcGinnis2006.number x✝¹, Minimalist.FeatureVal.case x✝]

The Vocabularies (27), (43), (44)

def GonzalezPootMcGinnis2006.agr3 : List (DistributedMorphology.VocabularyItem Minimalist.FeatureVal String)

The Agr3 Vocabulary Items (27), in scansion order.

Equations

• One or more equations did not get rendered due to their size.

def GonzalezPootMcGinnis2006.agr1 : List (DistributedMorphology.VocabularyItem Minimalist.FeatureVal String)

The Agr1 Vocabulary Items (43): the ergative auxiliary suffix.

Equations

• One or more equations did not get rendered due to their size.

def GonzalezPootMcGinnis2006.agr2 : List (DistributedMorphology.VocabularyItem Minimalist.FeatureVal String)

The Agr2 Vocabulary Items (44): the ergative verbal prefix.

Equations

• One or more equations did not get rendered due to their size.

def GonzalezPootMcGinnis2006.suffixes (subj : Person × Bool) (obj : Option (Person × Bool)) : List String

The overt verbal suffixes of a clause: Agr3 bears the subject's matrix and, in a transitive clause, the object's ((25), (28b)); strict scansion of (27) realizes them, and the elsewhere -Ø is not overt.

Equations

• One or more equations did not get rendered due to their size.

def GonzalezPootMcGinnis2006.templateSuffixes (subj obj : Person × Bool) : List String

The rival template (18): object agreement then subject agreement, each a node of its own realized by the Subset Principle over (27).

Equations

• One or more equations did not get rendered due to their size.

The data pool

structure GonzalezPootMcGinnis2006.Row : Type

A row of the pool: the arguments, the auxiliary suffix, the verbal prefix, the overt verbal suffixes, and the judgment.

• subj : Person × Bool
• obj : Option (Person × Bool)
• aux : String
• prefix_ : String
• suffixes : List String
• accepted : Bool

def GonzalezPootMcGinnis2006.instDecidableEqRow.decEq (x✝ x✝¹ : Row) : Decidable (x✝ = x✝¹)

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance GonzalezPootMcGinnis2006.instDecidableEqRow : DecidableEq Row

Equations

• GonzalezPootMcGinnis2006.instDecidableEqRow = GonzalezPootMcGinnis2006.instDecidableEqRow.decEq

def GonzalezPootMcGinnis2006.instReprRow.repr : Row → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance GonzalezPootMcGinnis2006.instReprRow : Repr Row

Equations

• GonzalezPootMcGinnis2006.instReprRow = { reprPrec := GonzalezPootMcGinnis2006.instReprRow.repr }

def GonzalezPootMcGinnis2006.personOfString : String → Option Person

Equations

• GonzalezPootMcGinnis2006.personOfString "1" = some Person.first
• GonzalezPootMcGinnis2006.personOfString "2" = some Person.second
• GonzalezPootMcGinnis2006.personOfString "3" = some Person.third
• GonzalezPootMcGinnis2006.personOfString x✝ = none

def GonzalezPootMcGinnis2006.Row.ofExample (ex : Data.Examples.LinguisticExample) : Option Row

Equations

• One or more equations did not get rendered due to their size.

theorem GonzalezPootMcGinnis2006.row_ofExample_isSome (ex : Data.Examples.LinguisticExample) : ex ∈ Examples.all → (Row.ofExample ex).isSome = true

def GonzalezPootMcGinnis2006.rows : List Row

Equations

• GonzalezPootMcGinnis2006.rows = List.filterMap GonzalezPootMcGinnis2006.Row.ofExample GonzalezPootMcGinnis2006.Examples.all

theorem GonzalezPootMcGinnis2006.suffixes_rows (r : Row) : r ∈ rows → (r.accepted = true) = (suffixes r.subj r.obj = r.suffixes)

Local Fission ((19)–(24), (16)): a row is grammatical iff its overt verbal suffixes are what strict scansion of (27) inserts — -éːʃ before -oʔob in both (20) and (22), -oʔob once in (24).

theorem GonzalezPootMcGinnis2006.template_predicts_starred (r : Row) : r ∈ rows → ∀ o ∈ r.obj, r.accepted = false → templateSuffixes r.subj o = r.suffixes

The template (18) predicts every starred form — -oʔob-éːʃ for (21), -oʔob-oʔob for (23).

theorem GonzalezPootMcGinnis2006.template_fails_grammatical : ∃ r ∈ rows, r.accepted = true ∧ ∃ o ∈ r.obj, templateSuffixes r.subj o ≠ r.suffixes

The template (18) fails a grammatical row — (22) and (24), whose orders it reverses or doubles — while fitting (19) and (20).

theorem GonzalezPootMcGinnis2006.aux_prefix_rows (r : Row) : r ∈ rows → DistributedMorphology.subsetPrinciple agr1 (DistributedMorphology.Neighborhood.ofBundle (ergMatrix r.subj.1 r.subj.2)) = some r.aux ∧ DistributedMorphology.subsetPrinciple agr2 (DistributedMorphology.Neighborhood.ofBundle (ergMatrix r.subj.1 r.subj.2)) = some r.prefix_

Agr1 (43) and Agr2 (44) recover the auxiliary suffix and verbal prefix of every row ((17), (39)).

theorem GonzalezPootMcGinnis2006.first_person_no_verbal_number (pl : Bool) : suffixes (Person.first, pl) none = []

A first-person ergative argument takes no verbal number suffix ((3)–(4)): its number is a person distinction, so no item of (27) matches beyond the elsewhere.